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PHOTOS: Clinton's life and career

Vice President Joe Biden is a way distant second with 13 percent, followed by New York Gov. Andrew Cuomo with 4 percent, while Massachusetts Gov. Deval Patrick; Maryland Gov. Martin O’Malley and Virginia Sen. Mark Warner each registered at 1 percent or less.

“Former Secretary of State Hillary Clinton has a rock-solid hold on the hearts of Democratic voters at this point,” said Quinnipiac Polling Institute assistant director Peter A. Brown. “There is a long way to go until 2016, but none of the other younger potential candidates for the Democratic nomination currently has anything approaching widespread support from party voters.”

But Brown noted that if Clinton were not run for president, Biden would be in a better position to run.

“If she decides not to run, [Biden] does almost as well as she does against the rest of the field,” Brown said in a statement.

Quinnipiac didn’t poll on potential GOP candidates in this particular poll. Quinnipiac polled 1,471 registered voters between April 25 and April 29, and it has a margin of error of plus or minus 2.6 percentage points.